Problem: Reduce to lowest terms: $- \dfrac{5}{4} \div \dfrac{3}{2} = {?}$
Solution: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{3}{2}$ is $ \dfrac{2}{3}$ Therefore: $ - \dfrac{5}{4} \div \dfrac{3}{2} = - \dfrac{5}{4} \times \dfrac{2}{3} $ $ \phantom{- \dfrac{5}{4} \times \dfrac{2}{3}} = \dfrac{-5 \times 2}{4 \times 3} $ $ \phantom{- \dfrac{5}{4} \times \dfrac{2}{3}} = \dfrac{-10}{12} $ The numerator and denominator have a common divisor of $2$, so we can simplify: $ \dfrac{-10}{12} = \dfrac{-10 \div 2}{12 \div 2} = -\dfrac{5}{6} $